Signal, Image and Video Processing

, Volume 10, Issue 5, pp 943–949 | Cite as

Three-dimensional interpolation methods to spatiotemporal EEG mapping during various behavioral states

  • Ibtihel Nouira
  • Asma Ben Abdallah
  • Mohamed Hedi Bedoui
Original Paper
First Online:
Received:
Revised:
Accepted:
  • 155 Downloads

Abstract

This work applies a novel method called multiquadratic interpolation that represents a 3D brain activity following a spatiotemporal mode. It also develops other classical interpolation techniques (barycentric, spline), which are based on the calculation of the Euclidean distance between the estimated and measured electrodes. Then, it modifies these methods by substituting the Euclidean distance by the corresponding arc length. Starting from 19 real electrodes for generating the electroencephalogram (EEG) potential representations of healthy subjects having three different behavioral brain states, a 3D EEG mapping of 128 electrodes was obtained. The proposed multiquadratic interpolation is evaluated by comparing it with the other methods by calculating the root mean squared error and processing time means.

Keywords

Brain activity 3D interpolation techniques Spatiotemporal mode Root mean squared error 
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References

  1. 1.
    Abdoun, O., Joucla, S., Mazzocco, C., Yvert, B.: NeuroMap: a spline-based interactive open-source software for spatiotemporal mapping of 2D and 3D MEA data. Front. Neuroinform. 4, 119 (2011)CrossRefGoogle Scholar
  2. 2.
    Fletcher, E.M., Kussmaul, C.L., Mangun, G.R.: Estimation of interpolation errors in scalp topographic mapping. Electroencephalogr. Clin. Neurophysiol. 98, 422–434 (1996)Google Scholar
  3. 3.
    Onaran, I., Ince, N.F., Cetin, A.E.: Sparse spatial filter via a novel objective function minimization with smooth \(l_{1}\) regularization. Biomed. Signal Process. Control 8, 282–288 (2013)CrossRefGoogle Scholar
  4. 4.
    Duffy, F.H., Bartels, P.H., Burchfiel, J.L.: Significance probability mapping: an aid in the topographic analysis of brain electrical activity. Electroencephalogr. Clin. Neurophysiol. 51, 455–462 (1981)CrossRefGoogle Scholar
  5. 5.
    Ashida, H., Tatsuno, J., Okamoto, J., Maru, E.: Field mapping of EEG by unbiased polynomial interpolation. J. Biomed. Inform. 17, 267–276 (1984)Google Scholar
  6. 6.
    Perrin, F., Pernier, J., Bertrand, O., Giard, M.H., Echallier, J.F.: Mapping of scalp potentials by surface spline interpolation. Electroencephalogr. Clin. Neurophysiol. 66, 75–81 (1987)CrossRefGoogle Scholar
  7. 7.
    Perrin, F., Pernier, J., Bertrand, O., Echallier, J.F.: Spherical splines for scalp potential and current density mapping. Electroencephalogr. Clin. Neurophysiol. 72, 184–187 (1989)CrossRefGoogle Scholar
  8. 8.
    Soufflet, L., Toussaint, M., Luthringer, R., Gresser, j, Minot, R., Macher, J.P.: A statistical evaluation of the main interpolation methods applied to 3-dimensional EEG mapping. Electroencephalogr. Clin. Neurophysiol. 79, 393–402 (1991)CrossRefGoogle Scholar
  9. 9.
    Srinivasan, R., Nunez, P.L., Tucker, D.M., Silberstein, R.B., Caducsh, P.J.: Spatial sampling and filtering of EEG with spline Laplacians to estimate cortical potentials. Brain Topogr. 8, 355–366 (1996)CrossRefGoogle Scholar
  10. 10.
    Ferree, T.C.: Spherical splines and average referencing in scalp electroencephalography. Brain Topogr. 19, 43–52 (2006)CrossRefGoogle Scholar
  11. 11.
    Brunet, D., Murray, M.M., Michel, C.M.: Spatiotemporal analysis of multichannel EEG: CARTOOL. Comput. Intell. Neurosci. 2011 (2011). doi: 10.1155/2011/813870
  12. 12.
    Lagarias, J.C., Reeds, J.A., Wright, M.H., Wright, P.E.: Convergence properties of the Nelder–Mead simplex method in low dimensions. SIAM J. Control Optim. 9, 112–147 (1998)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Law, S.K., Nunez, P.L., Wijesinghe, R.S.: High-resolution EEG using spline generated surface Laplacians on spherical and ellipsoidal surfaces. IEEE Trans. Bio-Med. Eng. 40, 145–153 (1993)CrossRefGoogle Scholar
  14. 14.
    Ferree, T.C.: Spline Interpolation of the Scalp EEG. Electrical Geodesics, Inc.,Technical Note(2000)Google Scholar
  15. 15.
    Yvert, B., Crouzeix-Cheylus, A., Jacques, P.: Fast realistic modeling in bioelectromagnetism using lead-field interpolation. Hum. Brain. Mapp. 14, 48–63 (2001)CrossRefGoogle Scholar
  16. 16.
    Franke, R., Neilson, G.: Scattered data interpolation and applications: a tutorial and survey. In: Hagen, H., Roller, D. (eds.) Geometric Modelling: Methods and Their Applications, pp. 131–160. Springer, Berlin (1991)Google Scholar

Copyright information

© Springer-Verlag London 2015

Authors and Affiliations

  1. 1.TIM LaboratoryMedicine Faculty of MonastirMonastirTunisia

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